Discrete multi-tone (DMT) modulation is used in many types of data communication systems, among them multi-carrier Very-high-speed Digital Subscriber Line (VDSL) modems, as well as Asymmetric DSL (ADSL). In these systems, N tones (also known as subcarriers) are modulated by QAM two-dimensional input frequency-domain symbols. A 2N-point Inverse Fast Fourier Transform (IFFT) then produces a corresponding time-domain symbol, expressed as a real baseband time-domain output signal of 2N real samples in each symbol period. At the receiving side, 2N samples are extracted from the time-domain signal during each symbol period. A FFT is used to demodulate the signal and recover the original QAM symbols on the N tones.
The number of bits to be encoded by each tone, known as the bit loading (or bit allocation), is determined by the receiver according to the line conditions, which are measured as a function of frequency during a training period. The bit-loading value for each tone may take any value from zero up to a preset maximum. The receiver passes a table of these values, known as the bit-loading table (or bit allocation table), to the transmitter, which thus determines how many bits of the input data stream to allocate to each successive tone in the tone order.
In some schemes, the transmitter simply encodes the tones in order of frequency. More advanced schemes, however, permit the receiver to determine the tone order arbitrarily. For example, the receiver may choose an interleaved tone order so that successive bits in the input data stream are carried by tones that are relatively far apart in frequency. Interleaved tone ordering may be combined with trellis coding for purposes of forward error correction, in order to prevent data loss due to narrowband interference. A scheme of this sort may be used, for example, in ADSL2 systems, as described in section 8.6 of ITU-T Recommendation G.992.3, entitled Series G: Transmission Systems and Media, Digital Systems and Networks; Digital Sections and Digital Line System—Access Networks; Asymmetric Digital Subscriber Line Transceivers 2 (ADSL2) (International Telecommunication Union, 2002), which is incorporated herein by reference. According to this scheme, the receiver determines a tone-order table listing the tones in the order in which they are to be encoded, and passes this table to the transmitter along with the bit-loading table.
The trellis coding scheme that is mandated by the above-mentioned ADSL2 standard uses a 16-state, four-dimensional trellis code, which accepts two-dimensional constellation points as inputs. In other words, each input to the trellis encoder must be at least two bits. The ADSL2 standard therefore requires that the bit-loading table include an even number of one-bit tones (i.e., tones i whose bit loading B(i)=1), and that these one-bit tones be grouped together at the end of the tone order. For this purpose, the transmitter must reorder the tone table that it received from the receiver to generate a reordered tone table with all the one-bit tones at the end of the table. The one-bit tones are then paired to form two-dimensional constellation points as input to the trellis encoder. The bit-loading table is reordered in accordance with the reordered tone table.